Inserted: 11 sep 2018
Last Updated: 22 jan 2020
Journal: Advances in Calculus of Variations
We consider two notions of functions of bounded variation in complete metric measure spaces, one due to Martio and the other due to Miranda Jr. We show that these two notions coincide, if the measure is doubling and supports a $1$-Poincaré inequality. In doing so, we also prove that if the measure is doubling and supports a $1$-Poincaré inequality, then the metric space supports a Semmes family of curves structure.